Unit 2 - Practice Quiz

The word "percent" is derived from the Latin phrase "per centum," which means "by the hundred." It represents a fraction of 100.

To convert a percentage to a fraction, you place the number over 100. So, . Simplifying this fraction by dividing both numerator and denominator by 50 gives .

To find the percentage of a number, convert the percentage to a decimal or fraction and multiply. . So, .

To convert a decimal to a percentage, you multiply the decimal by 100. So, .

To convert a fraction to a percentage, multiply the fraction by 100. So, .

To find what percentage one number is of another, use the formula . So, .

To express the score as a percentage, divide the score obtained by the total possible score and multiply by 100. .

100% of any number is the number itself, because , and .

Profit is made when an item is sold for more than it cost to purchase. The formula is Profit = SP - CP. If SP > CP, the result is positive, indicating a profit.

A loss is incurred when an item is sold for less than its purchase price (Cost Price). The formula is Loss = CP - SP. If CP > SP, the result is positive, indicating a loss.

The Cost Price (CP) is the original price of an item, which includes the cost of acquisition and any overhead expenses.

Profit is calculated as Selling Price minus Cost Price. Profit = SP - CP = $120 - $100 = $20.

Loss is calculated as Cost Price minus Selling Price. Loss = CP - SP = $200 - $180 = $20.

A discount is always calculated on the Marked Price (also known as the list price or tag price) of an item.

First, calculate the discount amount: of $50 = . Then, subtract the discount from the Marked Price: SP = MP - Discount = $50 - $5 = $45$.

Profit Percentage (or Gain Percentage) is always calculated with respect to the Cost Price (CP), as it measures the return on the original investment.

When the Cost Price is equal to the Selling Price, the transaction breaks even, meaning there is neither a profit nor a loss.

The Selling Price is the sum of the Cost Price and the Profit. SP = CP + Profit = $80 + $20 = $100.

The Marked Price (MP), or list price, is the price displayed on the article's label or tag by the manufacturer or seller.

To find the passing marks, calculate 40% of the total marks. of .

Let the initial price be and initial consumption be . The initial expenditure is .
New price .
Let the new consumption be . The expenditure must remain the same, so .
\n.
The reduction in consumption is .
Percentage reduction = .

Let the Cost Price (CP) be $100.
Marked Price (MP) is 40% above CP, so MP = $100 + 40\% \text{ of } 100 = 100 + 40 = $140.
Discount is 25% on MP. Discount amount = $25\% \text{ of } 140 = 0.25 \times 140 = $35.
Selling Price (SP) = MP - Discount = $140 - $35 = $105.
Gain = SP - CP = $105 - $100 = $5.
Gain Percent = .

Total number of votes = 7500.
Percentage of invalid votes = 20%.
Number of invalid votes = .
Number of valid votes = Total votes - Invalid votes = .
Winning candidate got 55% of the valid votes.
The other candidate got of the valid votes.
Votes for the other candidate = .

Let the Marked Price be MP.
The first discount is 10%, so the price becomes .
The second discount is 20% on the new price, so the final Selling Price (SP) is .
Given SP = $1440.
So, .
.

Let the monthly income be .
Spent on food = .
Remaining income = .
Of this remaining amount, he spends on rent and on conveyance. Total spending from remaining = .
Expenditure on rent and conveyance = .
Total expenditure = .
Savings = Income - Total expenditure = .
Given savings = $5400.
.
Income = I. Food = 0.3I. Remaining = 0.7I.
Rent = 40% of 0.7I = 0.28I. Remaining after rent = 0.7I - 0.28I = 0.42I.
Conveyance = 50% of 0.42I = 0.21I. Final Savings = 0.42I - 0.21I = 0.21I.
. This doesn't match. Let's try the other interpretation where 40% and 50% are parts of the first 'remaining'.
Remaining income = 0.7I. He spends 40% (of 0.7I) and 50% (of 0.7I). This is 90% of 0.7I. This leads to the first calculation which also didn't match. Let's assume the question meant "he spends 40% on rent and the remaining 50% on conveyance". This doesn't make sense. Let's assume the amounts are on different remainders. Let's assume the question meant 'Of the remaining, he spends 40% on rent and of the new remaining, he spends 50% on conveyance'.

Let's re-frame the question and solution to be clear.
Revised Question: Aman spends 30% of his income on food. Of the remaining amount, he spends 40% on rent. After spending on rent, he saves the remaining amount of $12,600. What is his monthly income? This is still not the same.

Let's go back to the original phrasing and assume the most common competitive exam interpretation: percentages of the remaining are calculated on the same remaining amount.
Income = I. Food = 0.3I. Remaining = 0.7I. From this 0.7I, he spends 40% on rent and 50% on conveyance. Total spent from remaining = (40%+50%) of 0.7I = 90% of 0.7I = 0.63I. Total spent = 0.3I + 0.63I = 0.93I. Savings = 0.07I. 0.07I=5400 => I is not integer.
Okay, the only logical interpretation that gives a clean answer is that the second and third percentages are of the original income. Let's test that.
Food: 30%. Rent: 40%. Conveyance: 50%. Total = 120%. Impossible.

Final attempt at interpretation: The question writer made a mistake. Let's assume it should be: "...Of the remaining, he spends 40% on rent. He saves the rest..." which is too simple. The numbers must be off. I will write a new question with this structure and correct numbers.

New Question: A person spends 20% of his income on food. Of the remaining, he spends 25% on rent and 30% on clothes. If he is left with $5400, what is his income?
Let income = I. Food = 0.2I. Remaining = 0.8I.
From this 0.8I, he spends 25% + 30% = 55%.
Spent on rent/clothes = 55% of 0.8I = 0.55 * 0.8I = 0.44I.
Total spent = 0.2I + 0.44I = 0.64I.
Savings = I - 0.64I = 0.36I.
.
.
Let's adjust the numbers to match one of the options. To get , savings must be . To get savings of 5400, I should be 15000. I'll change the options.

Revised Question and Solution for my own created problem:
Options: ["20,000", "12,000"]
Correct: "$15,000"
Explanation: Let total income be .
Spent on food = of .
Remaining income = .
From this remaining amount, total percentage spent on rent and clothes = .
Amount spent on rent and clothes = of .
Total savings = Remaining income - Amount spent on rent/clothes = .
Given savings = $5400$.
.

The dealer sells 900g but charges the customer for 1000g (1 kg). The cost price is for the amount he actually gives, while the selling price is for the amount he claims to give.
Let the cost price of 1 gram be $1.
Then, the cost price (CP) for the dealer is for 900g, so CP = $900.
The selling price (SP) he charges is for 1000g, so SP = $1000.
Profit = SP - CP = $1000 - $900 = $100.
Profit Percent = .

Let E be the set of students who passed in English and M be the set of students who passed in Mathematics.
, .
Percentage of students who failed in both subjects = 27%.
This means the percentage of students who passed in at least one subject is . So, .
Using the formula :


.
This means 62% of students passed in both subjects. Let the total number of students be T.
Given that 248 students passed in both subjects.
.
.

Let the Cost Price of 1 article be CP and the Selling Price of 1 article be SP.
According to the question, .
This can be rearranged to find the ratio of SP to CP: .
Let CP = and SP = for some constant .
Gain = SP - CP = .
Gain Percent = gain.

Present Value (P) = $50,000.
Value after 1st year (10% depreciation) = .
Value after 2nd year (20% depreciation on the new value) = .
Value after 3rd year (30% depreciation on the new value) = .
So, the final value is $25,200.

When two items are sold at the same selling price, one at a gain of and the other at a loss of , there is always an overall loss.
For the first article (15% gain): SP = $1955. CP1 = \frac{SP}{1.15} = \frac{1955}{1.15} = $1700.
For the second article (15% loss): SP = $1955. CP2 = \frac{SP}{0.85} = \frac{1955}{0.85} = $2300.
Total Cost Price = CP1 + CP2 = $1700 + $2300 = $4000.
Total Selling Price = $1955 + $1955 = $3910.
Overall Loss = Total CP - Total SP = .

Let B's income be 100.
A's income is 40% less than B's, so A's income = .
The difference between their incomes is .
To find how much B's income is more than A's, we calculate the percentage with respect to A's income.
Percentage = .

Let the Cost Price (CP) be $100.
Desired gain is 12%, so the Selling Price (SP) must be $100 + 12 = $112.
This SP is obtained after a 20% discount on the Marked Price (MP).
So, .
.
.
The Marked Price is 100.
Markup percentage = .

Initial mixture = 40 liters.
Initial quantity of water = liters.
Initial quantity of milk = liters.
Let liters of water be added. The quantity of milk remains unchanged.
New total volume = liters.
New quantity of water = liters.
We want the new water content to be 20%. This means the milk content will be 80%.
So, .
.
.
liters.

Let the Selling Price (SP) be $100.
Profit is 20% of SP, so Profit = $20\% \text{ of } 100 = $20.
The Cost Price (CP) is calculated as SP - Profit.
CP = $100 - $20 = $80.
The actual profit percentage is calculated on the Cost Price.
Actual Profit % = .

Let the number be .
The correct result should be .
The incorrect result obtained is .
The error = Correct Result - Incorrect Result = .
The percentage error is calculated with respect to the correct result.
Percentage Error = .

Let the initial costs of raw material, labor, and overheads be , and respectively.
Total initial cost = .
New raw material cost = .
New labor cost = .
New overheads cost = .
New total cost = .
Change in cost = .
Percentage change = increase.

Initial population = 160,000.
After 1st year (3% increase): Population = .
After 2nd year (2.5% increase): Population = .
After 3rd year (5% increase): Population = .
The present population is 177,366.

Total Cost Price (CP) = $6000.
Desired overall gain = 25%.
Desired total Selling Price (SP) = $6000 \times (1 + \frac{25}{100}) = 6000 \times 1.25 = $7500.
CP of the first half of goods = $\frac{6000}{2} = $3000.
These are sold at a 10% gain.
SP of the first half = $3000 \times (1 + \frac{10}{100}) = 3000 \times 1.1 = $3300.
CP of the remaining half = $3000.
Required SP for the remaining half = Total SP - SP of first half = $7500 - $3300 = $4200.
For the remaining half, CP = 4200.
Gain = $4200 - $3000 = $1200.
Gain Percent = .

Let the value two years ago be .
The depreciation rate is 10% per year.
Value after one year = .
Value after two years (present value) = .
Given the present value is $162,000.
So, .
.
The value two years ago was $200,000.

To solve this, we should compare the cost price and selling price for the same number of lemons. The LCM of 2 and 5 is 10.
Cost Price (CP) of 2 lemons = \frac{1}{2} \times 10 = $5.
SP of 5 lemons = 3/5. SP of 10 lemons = 6. This seems right.
Gain = SP - CP = 5 = $1.
CP of 1 lemon = 3/5 = $0.60.
Gain per lemon = $0.10.
Gain % = (0.10/0.50) 100 = (1/5) 100 = 20%.
Let's try: Buys at 3 for 3.
LCM of 3 and 2 is 6.
CP of 3 lemons = 4.
SP of 2 lemons = 9.
Gain = 4 = $5.
Gain % = (5/4) 100 = 125%.
Let's try to make it work for 50%.
We need (SP-CP)/CP = 1/2. So SP/CP - 1 = 1/2. SP/CP = 3/2.
Let's say he buys at 3 for $2 (CP per lemon = 2/3).
SP should be (3/2) (2/3) = 1.
Let's modify the question slightly.
New Question: A fruit seller buys lemons at 6 for a dollar and sells them at 4 for a dollar. What is his gain or loss percent?
LCM(6,4) = 12.
CP of 6 lemons = 2.
SP of 4 lemons = 3.
Gain = 2 = $1. Gain % = (1/2)*100 = 50%. This works.

Final question to be used:
"A fruit seller buys lemons at 6 for a dollar and sells them at 4 for a dollar. What is his gain percent?"
Options: ["20%", "30%", "40%", "50%"], Correct: "50%".
Explanation: "To compare profit, we find the cost and selling price for the same quantity of lemons. The LCM of 6 and 4 is 12.
Cost Price (CP): He buys 6 lemons for 1 \times 2 = $2.
Selling Price (SP): He sells 4 lemons for 1 \times 3 = $3.
Gain = SP - CP = $3 - $2 = $1.
Gain Percent = .

Let the cost price (CP) of 1000g of goods be Rs. 1000.

1. Markup: He marks up the price by 20%. So, the Marked Price (MP) for 1000g is Rs. 1000 * 1.20 = Rs. 1200.
2. Faulty Weight: He sells 900g but charges the customer the price for 1000g. So, his Selling Price (SP) for 900g of goods is Rs. 1200.
3. Actual Cost: The actual cost price (CP) of the 900g of goods he sold is Rs. 900 (since we assumed CP of 1g is Rs. 1).
4. Profit Calculation:
   • Profit = SP - CP = Rs. 1200 - Rs. 900 = Rs. 300.
   • Profit Percentage = (Profit / CP) 100 = (300 / 900) 100 = (1/3) * 100 = 33.33%.

Let E be the set of candidates who passed in English and M be the set of candidates who passed in Mathematics.

• Percentage passed in English, P(E) = 70%.
• Percentage passed in Mathematics, P(M) = 80%.
• Percentage failed in both = 10%. This means the percentage of candidates who passed in at least one subject is P(E U M) = 100% - 10% = 90%.
• We know the formula: P(E U M) = P(E) + P(M) - P(E ∩ M).
• 90% = 70% + 80% - P(E ∩ M).
• 90% = 150% - P(E ∩ M).
• P(E ∩ M) = 150% - 90% = 60%.
  This 60% represents the candidates who passed in both subjects.
• Let the total number of candidates be T.
• 60% of T = 144.
• 0.60 * T = 144.
• T = 144 / 0.6 = 1440 / 6 = 240.
  So, the total number of candidates was 240.

Let the Cost Price (CP) be Rs. 1400.

• Profit = 20%.
• Selling Price (SP) = CP (1 + Profit%) = 1400 (1 + 0.20) = 1400 * 1.2 = Rs. 1680.
• The discount is 12.5% or 1/8.
• The relationship between SP, Marked Price (MP), and discount is: SP = MP * (1 - Discount%).
• 1680 = MP (1 - 0.125) = MP 0.875.
• MP = 1680 / 0.875.
• To simplify, use fractions: 12.5% = 1/8. So SP = MP (1 - 1/8) = MP (7/8).
• 1680 = MP * (7/8).
• MP = (1680 * 8) / 7.
• Since 1680 / 7 = 240, MP = 240 * 8 = Rs. 1920.

First, convert the percentages to fractions for easier calculation:

• First year increase: . The multiplying factor is .
• Second year decrease: . The multiplying factor is .
• Third year increase: . The multiplying factor is .
  Let the initial population be P.
• Final Population = P (First year factor) (Second year factor) * (Third year factor).
• 1,10,000 = P () () * ().
• The 7s cancel out: 1,10,000 = P () = P ().
• P = 1,10,000 ()._n- P = () 48 = 2000 * 48 = 96,000.

SP2 = 0.9CP2. Total SP = 1.2CP1 + 0.9(1.2CP1) = 1.2CP1 + 1.08CP1 = 2.28CP1. Total CP = 2.2CP1. Profit = 0.08CP1. Profit % = (0.08/2.2)100 = 80/22 = 40/11 = 3.63% profit.
Let's re-read the options. Maybe there's a simpler setup. Let CP1 = 100. Then SP1 = 120. So CP2 = 120. SP2 = 120 0.8 = 96.
Total CP = CP1 + CP2 = 100 + 120 = 220.
Total SP = SP1 + SP2 = 120 + 96 = 216.
Loss = 220 - 216 = 4.
Loss % = (4/220) 100 = (1/55)100 = 20/11 = 1.81% Loss. The initial calculation was right, but none of the options match. Let's change the second loss to 15%.
SP2 = 0.85CP2. Total SP = 1.2CP1 + 0.85(1.2CP1) = 1.2CP1 + 1.02CP1 = 2.22CP1. Profit = 0.02CP1. Profit % = (0.02/2.2)100 = 20/22 = 10/11 = 0.9% profit.
Let's change first profit to 25%. SP1 = 1.25CP1, CP2 = 1.25CP1. Let second loss be 20%. SP2 = 0.8CP2 = 0.8(1.25CP1) = 1CP1. Total SP = 1.25CP1 + 1CP1 = 2.25CP1. Total CP = CP1 + 1.25CP1 = 2.25CP1. No profit, no loss. This is a good case. Let's make it more subtle. First profit 25%, second loss 16%. SP2=0.84CP2 = 0.84(1.25CP1) = 1.05CP1. Total SP = 1.25CP1 + 1.05CP1 = 2.3CP1. Total CP = 2.25CP1. Profit = 0.05CP1. Profit % = (0.05/2.25)*100 = 500/225 = 20/9 = 2.22% profit. Let's adjust the original question. If SP2 is at 10% loss, profit is 3.63%. I will rewrite the question to yield a clean answer.Let's modify the question slightly: An item passes through three hands. A sells to B at 20% profit. B sells to C at a loss of 25%. C sells to D for Rs. 2700 at a profit of 50%. What was the cost price for A?
My current Q5 is similar. Let's stick with the two-article problem and fix it.Let's fix the question as: A man sells two articles. The cost price of the first is equal to the selling price of the second. The first is sold at a 10% loss. The second is sold at a 25% profit. What is the overall profit or loss percentage?

1. CP1 = SP2.
2. SP1 = 0.9 * CP1.
3. SP2 = 1.25 CP2. So CP1 = 1.25 CP2 => CP2 = CP1 / 1.25 = 0.8 * CP1.
4. Total CP = CP1 + CP2 = CP1 + 0.8CP1 = 1.8CP1.
5. Total SP = SP1 + SP2 = 0.9CP1 + CP1 = 1.9CP1.
6. Profit = 1.9CP1 - 1.8CP1 = 0.1*CP1.
7. Profit % = (0.1CP1 / 1.8CP1) 100 = (1/18)100 = 50/9 = 5.55% Profit. This is a good hard question.Let's try to get a 2% profit.Let Total CP = X, Total SP = 1.02X.(CP1+CP2) 1.02 = SP1+SP2Let's go back to my initial question and re-read. Maybe I misunderstood it.A man sells two articles. The selling price of the first is equal to the cost price of the second. The first is sold at a 20% profit, and the second is sold at a 20% loss.CP1=100. SP1=120. CP2=120. SP2=1200.8=96. Total CP = 100+120=220. Total SP = 120+96=216. Loss=4. Loss% = 4/220 100 = 1.81% Loss.The calculation is correct. The options are wrong. I'll correct the options and explanation.Let's try to construct a question for 2% profit.Let P = (SP1+SP2)/(CP1+CP2) - 1 = 0.02.Let CP1=100. Let SP1 = 120 (20% profit). CP2=120.Total CP = 220. Target Total SP = 220 1.02 = 224.4.SP1=120. So SP2 = 224.4 - 120 = 104.4.Loss on 2nd item = CP2 - SP2 = 120 - 104.4 = 15.6.Loss % on 2nd = (15.6/120)100 = 156/12 = 13%.So the question would be: ...first sold at 20% profit, second at 13% loss. This makes the calculation hard.Let's just use my 5.55% profit question.Ok, I will go back to a question I made before and check the math.A sells an article to B at a 20% profit. B sells it to C at a 25% profit. C sells it to D for Rs. 225, incurring a loss of 25%. What was the cost price of the article for A?CP_A = x. CP_B = 1.2x. CP_C = 1.2x 1.25 = 1.5x. SP_C = 1.5x 0.75 = 1.125x.1.125x = 225 => x = 225 / 1.125 = 225 / (9/8) = 225 8 / 9 = 25 * 8 = 200. This is a good one. Let's use it.

Let T be the total number of votes on the voter list.

• Votes not cast = 10% of T = 0.1T.
• Votes polled = T - 0.1T = 0.9T.
• Winner's votes = 47% of T = 0.47T.
• Valid votes = Votes polled - Invalid votes = 0.9T - 60.
• Loser's votes = Valid votes - Winner's votes = (0.9T - 60) - 0.47T = 0.43T - 60.
• The winner won by 460 votes, so: Winner's votes - Loser's votes = 460.
• (0.47T) - (0.43T - 60) = 460.
• 0.04T + 60 = 460.
• 0.04T = 400.
• T = 400 / 0.04 = 10,000.
• The total number of voters on the list is 10,000.
• The question asks for the total number of votes polled.
• Votes polled = 90% of T = 0.9 * 10,000 = 9,000.

Let the Cost Price be CP.

• Case 1 (Profit): SP = Rs. 900. Profit = SP - CP = 900 - CP.
• Case 2 (Loss): SP = Rs. 450. Loss = CP - SP = CP - 450.
• According to the question, Profit = 2 * Loss.
• 900 - CP = 2 * (CP - 450).
• 900 - CP = 2CP - 900.
• 900 + 900 = 2CP + CP.
• 1800 = 3CP.
• CP = Rs. 600.
• Now, to make a 25% profit, the new SP should be:
• New SP = CP (1 + 25%) = 600 1.25 = 600 (5/4) = 150 5 = Rs. 750.

The key is that the quantity of acid remains constant before and after adding water.

1. Initial State:
   • Total solution = 60 litres.
   • Acid percentage = 80%.
   • Quantity of acid = 80% of 60 = 0.80 * 60 = 48 litres.
   • Quantity of water = 60 - 48 = 12 litres.
2. Final State:
   • Let 'w' be the amount of water added.
   • New total solution = 60 + w litres.
   • The quantity of acid is still 48 litres.
   • The new percentage of acid is 60%.
   • So, 60% of (60 + w) = 48.
   • 0.60 * (60 + w) = 48.
   • 60 + w = 48 / 0.6 = 480 / 6 = 80.
   • w = 80 - 60 = 20 litres.
     Therefore, 20 litres of water must be added.

Let the marked price (MP) of one item be Rs. 100.

1. First Offer (Buy 4, Get 1 Free):
   • The customer gets 5 items but pays for 4.
   • Total MP of 5 items = 5 * 100 = Rs. 500.
   • Amount paid = 4 * 100 = Rs. 400.
   • This is equivalent to a discount of (500 - 400) / 500 = 100 / 500 = 20%. Let's call this D1.
2. Second Offer (10% further discount):
   • This discount is applied to the price after the first offer, which is Rs. 400.
   • Further discount = 10% of 400 = Rs. 40. Let's call this D2.
3. Net Effective Discount:
   • We can use the successive discount formula: D_eff = D1 + D2 - (D1 * D2 / 100).
   • D_eff = 20 + 10 - (20 * 10 / 100) = 30 - 2 = 28%.
   • Alternatively:
   • Final SP = 400 - 40 = Rs. 360.
   • Total MP was Rs. 500.
   • Total discount = 500 - 360 = Rs. 140.
   • Effective discount % = (140 / 500) * 100 = 28%.

The core principle is that the amount of solid pulp remains constant during the drying process.

1. In Fresh Grapes:
   • Water = 90%, so Pulp = 100% - 90% = 10%.
   • Total weight of fresh grapes = 20 kg.
   • Weight of pulp in fresh grapes = 10% of 20 kg = 0.10 * 20 = 2 kg.
2. In Dried Grapes:
   • Water = 20%, so Pulp = 100% - 20% = 80%.
   • The weight of pulp remains the same, so the dried grapes also contain 2 kg of pulp.
   • Let W_dry be the total weight of the dried grapes.
   • 80% of W_dry = 2 kg.
   • 0.80 * W_dry = 2.
   • W_dry = 2 / 0.8 = 20 / 8 = 2.5 kg.

Wait, let me re-check the calculation. Total SP = 750. Total CP = 600. Profit = 150. Profit % = 150/600 = 1/4 = 25%. Let me check my options and calculation. The calculation is correct. Let me adjust the option or the question. Let's make the third discount 50%. SP3 = 150 0.5 = 75. Total SP = 300+360+75 = 735. Profit = 135. Profit % = 135/600 100 = 135/6 = 22.5%. Not clean.Let's make the second discount 30%. SP2 = 3 (150 0.7) = 3 105 = 315. Rest discount 40%. SP3 = 1 90. Total SP = 300+315+90 = 705. Profit = 105. Profit % = 105/600 * 100 = 17.5%.Let's return to the original calculation. Total SP is 750. Total CP is 600. Profit is 150. Profit % is 25%. I will change the correct option to 25%.

Let the original radius be 'r'. The new radius 'r_new' = r * (1 + 10%) = 1.1r.

1. Surface Area (A = 4πr²):

   • Original Area: .
   • New Area: .
   • The area has increased by a factor of 1.21.
   • Percentage increase = (1.21 - 1) 100 = 0.21 100 = 21%.

2. Volume (V = 4/3 πr³):

   • Original Volume: .
   • New Volume: .
   • The volume has increased by a factor of 1.331.
   • Percentage increase = (1.331 - 1) 100 = 0.331 100 = 33.1%.

Let the cost prices of the two watches be CP1 and CP2.

• Given: CP1 + CP2 = 4800.
• Watch 1 (Loss): Sold at 15% loss. SP1 = CP1 (1 - 0.15) = 0.85 CP1.
• Watch 2 (Gain): Sold at 19% gain. SP2 = CP2 (1 + 0.19) = 1.19 CP2.
• Given: SP1 = SP2.
• Therefore, 0.85 CP1 = 1.19 CP2.
• To simplify, multiply by 100: 85 CP1 = 119 CP2.
• Both 85 and 119 are divisible by 17: (17 5) CP1 = (17 7) CP2.
• 5 CP1 = 7 CP2 => CP1 / CP2 = 7 / 5.
• This means CP1 and CP2 are in the ratio 7:5.
• The sum of the ratio parts is 7 + 5 = 12.
• We need to find the cost price of the watch sold at a loss, which is CP1.
• CP1 = (Total Cost) (Ratio part of CP1) / (Sum of ratio parts) = 4800 (7 / 12) = 400 * 7 = Rs. 2800.

Let the total sales be S. The amount remitted is Total Sales - Commission.
Let's assume the sales S are greater than Rs. 10,000.

• Commission on the first Rs. 10,000 = 10% of 10,000 = Rs. 1000.
• Commission on the sales exceeding Rs. 10,000 = 5% of (S - 10,000) = 0.05(S - 10,000).
• Total Commission = 1000 + 0.05(S - 10,000).
• Amount Remitted = Total Sales (S) - Total Commission.
• 48,500 = S - [1000 + 0.05(S - 10,000)].
• 48,500 = S - 1000 - 0.05S + 500.
• 48,500 = 0.95S - 500.
• 49,000 = 0.95S.
• S = 49,000 / 0.95 = 49000 / (19/20) = 49000 * 20 / 19.
• S = (49000/19) * 20. This gives a non-integer value, something is wrong.
  Let's re-read the question carefully. He remits Rs. 48,500.Let's check the options. Say Total Sales = 51,000.- Commission on first 10,000 = 1000.- Commission on remaining 41,000 = 5% of 41,000 = 2050.- Total Commission = 1000 + 2050 = 3050.- Amount remitted = 51000 - 3050 = 47950. Close. Maybe the question is commission is 5% on total sales and an additional 5% bonus on sales above 10,000? No.Let's check my equation: 48,500 = S - [1000 + 0.05S - 500] = S - 1000 - 0.05S + 500 = 0.95S - 500. 49000 = 0.95S. S=51578.9. The problem statement or the options must be flawed. Let's adjust the problem for a clean answer.
  Let the second commission be 4%. Remit = 48,900.
  48,900 = S - [1000 + 0.04(S - 10000)] = S - 1000 - 0.04S + 400 = 0.96S - 600.
  49,500 = 0.96S. S = 49500 / 0.96 = 51562.5. Still not good.
  Let's assume the question meant commission of 10% on first 10k, and 5% of total sales if sales > 10k. No, that's not standard.
  Let's try to work backwards from the answer Rs. 51,000. Commission = 3050. Remitted = 47950. The question should have He remits Rs. 47,950. I will correct the question's value.
  New Question: A salesman's commission is 10% on all sales up to Rs. 10,000 and 5% on all sales exceeding this. He remits Rs. 47,950 to his company after deducting his commission. What were the total sales?
  Explanation:
  Let total sales be S (> 10,000).
  Commission = 10% on 10,000 + 5% on (S - 10,000)
  Commission = 1000 + 0.05S - 500 = 500 + 0.05S
  Remitted Amount = S - Commission
  47,950 = S - (500 + 0.05S)
  47,950 = 0.95S - 500
  48,450 = 0.95S
  S = 48450 / 0.95 = 51,000.

Let CP be the cost price of one article and SP be the selling price of one article.

• Given: .
• From this, we can find the ratio of SP to CP: .
• The profit percentage is given by the formula: Profit % = .
• Given profit is 25%.
• .
• .
• .
• .
• ._n- Therefore, the value of is 16.

Let's assume C's salary is Rs. 100.

1. Calculate B's salary:
   • B's salary is 25% of C's salary.
   • B = 0.25 C = 0.25 100 = Rs. 25.
2. Calculate A's salary:
   • A's salary is 40% of B's salary.
   • A = 0.40 B = 0.40 25 = Rs. 10.
3. Compare C's salary to A's salary:
   • C's salary = Rs. 100.
   • A's salary = Rs. 10.
   • The difference is C - A = 100 - 10 = Rs. 90.
4. Calculate the percentage:
   • The question asks by what percentage C's salary is more than A's salary. The base for the percentage is A's salary.
   • Percentage more = (Difference / A's salary) 100 = (90 / 10) 100 = 9 * 100 = 900%.

Wait, my calculation gives 400. Let me check the options.Maybe the question intended for a different answer. Let's try to get 600.If CP = 600, SP = 720.New CP = 540. New SP = 720 - 12 = 708.New Profit = 708 - 540 = 168.New Profit % = (168/540) * 100 = (1680/54) = 31.11%. It does not match.
My calculation is correct and the answer is 400. I will change the correct option. It seems I made an error in the option list.

First, we need to find the total marks for the examination.

1. Find Passing Marks:
   • The first student got 150 marks and failed by 25 marks.
   • This means the passing marks = 150 + 25 = 175 marks.
2. Find Total Marks:
   • The passing mark (175) is 35% of the total marks.
   • Let the total marks be T.
   • 0.35 * T = 175.
   • T = 175 / 0.35 = 17500 / 35 = 500.
   • The total marks for the exam are 500.
3. Calculate Percentage for the Second Student:
   • The second student scored 243 marks.
   • Percentage = (Marks Obtained / Total Marks) * 100.
   • Percentage = (243 / 500) * 100 = 243 / 5 = 48.6%.

Let the original Selling Price be SP and the Cost Price be CP.

1. Scenario with a loss:
   • The article is sold at a new price, SP_new = 80% of SP = 0.8 * SP.
   • At this price, there is a loss of 10%.
   • This means SP_new = CP (1 - 10%) = 0.9 CP.
2. Relate SP and CP:
   • We can equate the two expressions for SP_new:
   • 0.8 SP = 0.9 CP.
   • SP / CP = 0.9 / 0.8 = 9 / 8.
3. Calculate Original Profit:
   • The ratio SP/CP = 9/8 tells us that if CP is 8 units, SP is 9 units.
   • Profit = SP - CP = 9 - 8 = 1 unit.
   • Profit Percentage = (Profit / CP) * 100.
   • Profit % = (1 / 8) * 100 = 12.5%.
     So, the profit at the original selling price is 12.5%.

This is a classic problem where the product of two quantities (Price × Consumption) must remain constant.
Let the initial Price be P and initial Consumption be C. Initial Expenditure E = P × C.

• New Price: The price increases by 25%. New Price P' = P * (1 + 0.25) = 1.25P.
• New Consumption: Let the new consumption be C'.
• Expenditure remains constant: The new expenditure E' must be equal to the initial expenditure E.
• P' × C' = P × C.
• (1.25P) × C' = P × C.
• 1.25 × C' = C.
• C' = C / 1.25 = C / (5/4) = (4/5)C = 0.8C.
• The new consumption is 0.8 times the original consumption, which means it has been reduced.
• Reduction in Consumption: Original C - New C' = C - 0.8C = 0.2C.
• Percentage Reduction: (Reduction / Original Consumption) 100 = (0.2C / C) 100 = 20%.